### 物理代写|宇宙学代写cosmology代考|PHYC90009

statistics-lab™ 为您的留学生涯保驾护航 在代写宇宙学cosmology方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写宇宙学cosmology代写方面经验极为丰富，各种代写宇宙学cosmology相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|宇宙学代写cosmology代考|The concordance model of cosmology

Einstein’s discovery of general relativity in the previous century enabled us, for the first time in history, to come up with a compelling, testable theory of the universe. The realization that the universe is expanding and was once much hotter and denser allows us to modernize the deep age-old questions “Why are we here?” and “How did we get here?” The updated versions are now “How did the elements form?”, “Why is the universe so smooth?”, and “How did galaxies form within this smooth universe?” Remarkably, these questions and many like them have quantitative answers, answers that can be found only by combining our knowledge of fundamental physics with our understanding of the conditions in the early universe. Even more remarkably, these answers can be tested against astronomical observations. Before going into depth, we begin with a broad-brush overview of our current state of knowledge on the history of the universe in this chapter and the next.
The success of the Big Bang paradigm rests on a number of observational pillars: the Hubble diagram that measures expansion; light element abundances that are in accord with Big Bang Nucleosynthesis; temperature and polarization anisotropies in the cosmic microwave background that agree well with theory; and multiple probes of large-scale structure that also agree with the concordance model that will be described in this Chapter. This success has come at a price, however: we are now forced to introduce several ingredients that go beyond the Standard Model of particle physics (for a quick overview, see Box 1.1):

• dark matter and dark energy, which together dominate the energy budget of the universe over most of its lifetime;
• a mechanism generating the small initial perturbations out of which structure formed, the most popular explanation being inflation.

## 物理代写|宇宙学代写cosmology代考|A nutshell history of the universe

We have solid evidence that the universe is expanding. This means that early in its history the distance between us and distant galaxies was smaller than it is today. It is convenient to describe this effect by introducing the scale factor $a$, whose present value is set to 1 by convention. At earlier times, $a$ was smaller than it is today. We can imagine placing a grid in space as in Fig. 1.1 which expands uniformly as time evolves. Points on the grid, which correspond to observers at rest, maintain their coordinates, so the comoving distance between two points-which just measures the difference between coordinates, and can be obtained by counting grid cells as indicated in Fig. 1.1-remains constant. However, the physical distance is proportional to the scale factor, and the physical distance does evolve with time.
A directly related effect is that the physical wavelength of light emitted from a distant object is stretched out proportionally to the scale factor, so that the observed wavelength is larger than the one at which the light was emitted. It is convenient to define this stretching factor as the redshift $z$ :
$$1+z \equiv \frac{\lambda_{\text {obs }}}{\lambda_{\text {emit }}}=\frac{a_{\text {obs }}}{a_{\text {emit }}}=\frac{1}{a_{\text {emit }}} .$$
In addition to the scale factor and its evolution, the smooth universe is characterized by one other parameter, its geometry. There are three possibilities: Euclidean, open, or closed universes. These different possibilities are best understood by considering two freely traveling particles which start their journeys moving parallel to each other. In a Euclidean universe, often also called a “flat universe,” the particles behave as Euclid himself expected them to: their trajectories remain parallel as long as they travel freely. If the universe is closed, the initially parallel particles gradually converge, just as in the case of the 2 -sphere all lines of constant longitude meet at the North and South Poles. The analogy of a closed universe to the surface of a sphere runs even deeper: both are spaces of constant positive curvature, the former in three spatial dimensions and the latter in two. Finally, in an open universe, the initially parallel paths diverge, as would two marbles rolling off a saddle.

General relativity connects geometry to energy. Accordingly, the total energy density in the universe determines the geometry: if the density is higher than a critical value, $\rho_{\mathrm{cr}}$, which we will soon see is approximately $10^{-29} \mathrm{~g} \mathrm{~cm}^{-3}$, the universe is closed; if the density is lower, it is open. A Euclidean universe is one in which the energy density is precisely equal to critical. This seems unlikely to happen, and yet all observations indicate that the universe is Euclidean to within errors! We will later see that inflation provides a natural explanation for this fact.

## 物理代写|宇宙学代写cosmology代考|The Hubble diagram

If the universe is expanding as depicted in Fig. 1.1, then galaxies should be moving away from each other. We should therefore see galaxies receding from us. Hubble (1929) first found that distant galaxies are in fact all apparently receding from us, i.e. redshifted. He also noticed the trend that the velocity increases with distance. This is exactly what we expect in an expanding universe, for the physical distance between two galaxies is $d=a x$ where $x$ is the comoving distance. ${ }^{1}$ In the absence of any comoving motion, $\dot{x} \equiv d x / d t=0$ (no peculiar velocity), the relative velocity $v$ is therefore equal to
$$v=\frac{d}{d t}(a x)=\dot{a} x=H_{0} d \quad(v \ll c),$$
where overdots indicate derivatives with respect to time $t$. Therefore, the apparent velocity should increase linearly with distance (at least at low redshift) with a slope given by $H_{0}$, the Hubble constant. Eq. (1.8) is known as the Hubble-Lemaitre law. The value of the constant is simply determined by measuring the slope of the line in the Hubble diagram shown in Fig. 1.5.

In the next chapter, we will generalize the distance-redshift relation to larger distances, where Eq. (1.8) breaks down. Instead of recession velocities, this more rigorous derivation will be based on the stretching of the wavelength of light encoded in Eq. (1.1). For now, let us just point out that the distance-redshift relation depends on the energy content of the universe. Data from a variety of sources point to a current best-fit scenario that is Euclidean and contains about $70 \%$ of the energy in the form of a cosmological constant, or some other form of dark energy. This now forms the concordance cosmology that will be our working model throughout.

## 物理代写|宇宙学代写cosmology代考|The concordance model of cosmology

• 暗物质和暗能量，它们在宇宙生命的大部分时间里共同支配着宇宙的能量收支；
• 一种产生微小初始扰动的机制，形成结构，最流行的解释是暴胀。

## 物理代写|宇宙学代写cosmology代考|A nutshell history of the universe

1+和≡λ观测值 λ发射 =一个观测值 一个发射 =1一个发射 .

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。